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a_sh-v [17]
3 years ago
11

Find vertex of f(x)=x^2+6x+10

Mathematics
1 answer:
dem82 [27]3 years ago
5 0
You can see answer at photo! If you have any questions, write me in Telegram @ef1m0ff

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I have completed the first three parts of this question, but now need help to finish...I need to calculate the ratios of the 4 l
galben [10]

At first, we will find the lengths of LK, Lm, ON, OP, then use them to find the ratios between them

The rule of the distance is

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

For LK

Since L = (3, 6), K = (1,5.33), then

\begin{gathered} LK=\sqrt{(3-1)^2+(6-5.33)^2} \\ LK=\sqrt{4+0.4489} \\ LK=\sqrt{4.4489} \end{gathered}

For LM

Since L = (3, 6), M = (5, 6.67), then

\begin{gathered} LM=\sqrt{(3-5)^2+(6-6.67)^2} \\ LM=\sqrt{4+0.4489} \\ LM=\sqrt{4.4489} \end{gathered}

For ON

Since O = (3, 2.59) and N = (5, 4.2), then

\begin{gathered} ON=\sqrt{(3-5)^2+(2.59-4.2)} \\ ON=\sqrt{4+2.5921} \\ ON=\sqrt{6.5921} \end{gathered}

For OP

Since O = (3, 2.59), P = (1, 0.99), then

\begin{gathered} OP=\sqrt{(3-1)^2+(2.59-0.99)^2} \\ OP=\sqrt{4+2.56} \\ OP=\sqrt{6.56} \end{gathered}

Now let us find the ratios between them

\begin{gathered} \frac{KL}{LM}=\frac{\sqrt{4.4489}}{\sqrt{4.4489}}=1 \\ \frac{PO}{ON}=\frac{\sqrt{6.56}}{\sqrt{6.5921}}=0.9975\approx1 \\ \frac{KL}{LM}=\frac{PO}{ON}=1 \end{gathered}

That means, Parallel lines intercept equal parts

By joining MP

We will have Triangle KPM

Since KL = LM ------- Proved using the distance formula

Since LQ // KP ------ Given

Then MQ = QP ------- Using the theorem down

The theorem

If a line is drawn from a midpoint of one side of a triangle parallel to the opposite side, then it will intersect the 3rd side in its midpoint (Q is the midpoint of MP)

Parallel lines intercept equal parts

7 0
1 year ago
Which box shows a relationship where the constant of proportionality is 64?
Sever21 [200]

Answer:

C

Step-by-step explanation:

Constant of proportionality = \frac{y}{x}

Let's find out which if the boxes will give us 64 as constant of proportionality.

A. \frac{y}{x} = \frac{11}{2} = 5.5 ≠ 64

B. \frac{y}{x} = \frac{5}{15} = \frac{1}{3} ≠ 64

C. \frac{y}{x} = \frac{16}{\frac{1}{4}} = 16*\frac{4}{1} = 64 ≠ 64

D. \frac{y}{x} = \frac{\frac{3}{7}}{3} = \frac{3}{7}*\frac{1}{3} = \frac{1}{7} ≠ 64

E. \frac{y}{x} = \frac{2}{-10} = -\frac{1}{5} ≠ 64

F. \frac{y}{x} = \frac{21}{6} = \frac{7}{2} ≠ 64

G. \frac{y}{x} = \frac{4}{8} = \frac{1}{2} ≠ 64

From the boxes given, box C is the only box that shows us a relationship where the constant of proportionality is 64.

7 0
3 years ago
the drill must go 3/8 of the way through the sheet the sheet is 2.5 cm thick how deep should the drill be set
andrey2020 [161]

Answer:

15/16 cm

Step-by-step explanation:

The drill must go 3/8 of the way from one side of the sheet to the other.  The depth that this drill must reach is found by multiplying 2.5 cm by 3/8:

25       3       5         3

----- * ----- = ------ * ------ = 15/16 cm

10       8        2        8

7 0
3 years ago
What is 3 3/8 tons equal to in pounds?
guapka [62]

1 ton is equivalent to 2000 pounds

we have to find how many pounds 3 3/8 tons are equal to

if 1 ton --> 2000 pounds

we can break down the fraction into 3 + 3/8

then 3 tons --> 2000 x 3 = 6000 pounds

3/8 ton ---> 2000 x 3/8 = \frac{3*2000}{8} = \frac{6000}{8} = 750 pounds

after adding 6000 + 750 = 6750 pounds

answer is 6750 pounds

7 0
3 years ago
Read 2 more answers
There are 25 students in a class and 10 of the students past their algebra test what percentage of the students pass to the test
densk [106]
25 students.....10 of which passed...
percentage of students that passed : 10/25 = 0.4 = 40% <==
6 0
3 years ago
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